## Abstract

We present an average case analysis of two variants of dual-pivot quicksort, one with a non-algorithmic

comparison-optimal partitioning strategy, the other with a closely related algorithmic strategy. For both

we calculate the expected number of comparisons exactly as well as asymptotically, in particular, we

provide exact expressions for the linear, logarithmic, and constant terms. An essential step is the analysis

of zeros of lattice paths in a certain probability model. Along the way a combinatorial identity is proven.

comparison-optimal partitioning strategy, the other with a closely related algorithmic strategy. For both

we calculate the expected number of comparisons exactly as well as asymptotically, in particular, we

provide exact expressions for the linear, logarithmic, and constant terms. An essential step is the analysis

of zeros of lattice paths in a certain probability model. Along the way a combinatorial identity is proven.

Original language | English |
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Title of host publication | Proceedings of the 27th Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms |

Number of pages | 13 |

Publisher | Jagiellonian University in Krakow |

Publication date | 4 Jul 2016 |

Publication status | Published - 4 Jul 2016 |

Event | International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms - Jagiellonian University, Kraków, Poland Duration: 4 Jul 2016 → 7 Jul 2016 Conference number: 27 http://www.aofa2016.meetings.pl/ |

### Conference

Conference | International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms |
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Number | 27 |

Location | Jagiellonian University |

Country/Territory | Poland |

City | Kraków |

Period | 04/07/2016 → 07/07/2016 |

Internet address |

## Keywords

- Dual-pivot quicksort
- Average case analysis
- Comparison-optimal partitioning
- Algorithmic strategy
- Lattice paths analysis